Nucleon Pair Research Articles

Evidence for X(3872) in PbPb collisions and studies of its prompt production at [formula omitted

The first evidence for X(3872) in heavy ion collisions is reported. Prompt X(3872) production is studied with the CMS detector in PbPb collisions at a center-of-mass energy of sNN=5.02TeV per nucleon pair, using the decay chain X(3872)→ J/ψπ+π− → μ+μ−π+π−. The measurement is performed in a kinematic range in which the X(3872) candidates have a transverse momentum 15 <pT < 50GeV/c and rapidity |y| < 1.6. The statistical significance of the X(3872) signal is in excess of 3 standard deviations. The production and survival of the prompt X(3872) in the quark-gluon plasma is expected to depend upon its internal structure. The ratio of the X(3872) and ψ(2S) yields is found to be R = 1.10 ± 0.51 (stat.) ± 0.53 (syst.) and is compared to the ratio measured in pp collisions at s=7and8TeV.

Bottomonium production in Pb + Pb collisions with ATLAS

Bottomonium, a bound state of a bottom quark and its antiquark, is an excellent probe of the hot and dense medium created in heavy-ion collisions. The ATLAS collaboration at the LHC collected two large datasets of pp and Pb + Pb collisions in 2017 and 2018 corresponding to integrated luminosities of 0.26 fb−1 and 1.38 nb−1 respectively, at a center-of-mass energy per nucleon pair of 5.02 TeV. Bottomonium states are reconstructed via the dimuon decay channel in the absolute rapidity range of |y| < 1.5, and their production in Pb + Pb collisions is compared to that in pp collisions to extract the nuclear modification factor, RAA, as a function of transverse momentum, absolute rapidity, and event centrality. In addition, the relative suppression of the excited states ϒ(nS) to the ground state ϒ(1S) is studied.

High-Momentum Correlated Nucleons, Tensor Blocking, and Nuclear Shell Structure

Studies of light neutron-rich nuclei revealed many new phenomena in nuclear structures and reactions. One of the most important recent discoveries is the change of magic numbers. Traditional magic numbers (2, 8, 20, 28, 50, 128) have been understood by the spin-orbit coupling in the mean-field potential and they provide the base of nuclear shell model. Recently, however, it was found that some of those magic numbers (N=8, 20) disappear in neutron-rich nuclei. On the other hand, new magic numbers (N=6, 14, 16, 32 and 34) emerge in neutron-rich nuclei. In the present paper, it is shown that tensor correlations give notable effects to such new structures. In nuclei a large amount of binding energy is gained by high-momentum correlated pairs of nucleons due to the tensor interaction. Such tensor correlations strongly depend on the configuration space available for exciting the 2p-2h states. When additional neutrons occupy a new orbital, the previously available 2p-2h configurations may be blocked, resulting in a sudden loss of binding energy otherwise gained by the 2p-2h excitations. Such tensor blocking effects enlarge the energy gaps at all the observed new magic numbers.

Effective (kinetic freeze-out) temperature, transverse flow velocity, and kinetic freeze-out volume in high energy collisions

The transverse momentum spectra of different types of particles produced in central and peripheral gold-gold (Au-Au) and (inelastic) proton-proton ($pp$) collisions at the Relativistic Heavy Ion Collider (RHIC), as well as in central and peripheral lead-lead (Pb-Pb) and $pp$ collisions at the Large Hadron Collider (LHC) are analyzed by the standard distribution in terms of multi-component. The obtained results from the standard distribution give an approximate agreement with the measured experimental data by the STAR, PHENIX and ALICE Collaborations. The methodical behavior of the effective (kinetic freeze-out) temperature, transverse flow velocity and kinetic freeze-out volume with the mass dependence for different particles is obtained, which observes the early kinetic freeze-out of heavier particles as compared to the lighter particles. The parameters for emissions of different particles are observed to be different, which reveals a direct signature of the mass dependent differential kinetic freeze-out. It is also observed that the peripheral nucleus-nucleus ($AA$) and $pp$ collisions at the same center-of-mass energy per nucleon pair are close in terms of the extracted parameters.

Relativistic rank-one separable kernel for helium-3 charge form factor

Elastic electron-helium-3 scattering is studied in the relativistic impulse approximation. The amplitudes for the three-nucleon system are obtained by solving the relativistic generalization of the Faddeev equations with a separable rank-one kernel of the nucleon-nucleon interaction. The contribution of partial-wave states with nonzero orbital moment of a nucleon pair is investigated. The static approximation and additional relativistic corrections for the He3 charge form factor are calculated for the momentum transfer squared up to 100 fm−2. The contribution of the D13 partial-wave state and relativistic corrections are found to be sizable at high energies.

Exact sum rules with approximate ground states

Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree–Fock, projected Hartree–Fock, and the nucleon pair approximation. These approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.

Finite particle number description of neutron matter using the unitary correlation operator and high-momentum pair methods * *Supported by the National Natural Science Foundation of China (11822503, 11575082, 11947220), by the Fundamental Research Funds for the Central Universities (Nanjing University), by JSPS KAKENHI (JP18K03660, JP16K05351), and by a Project funded by China Postdoctoral Science Foundation (2019M661785). The author N. W.

Using bare Argonne V4' (AV4'), V6' (AV6'), and V8' (AV8') nucleon–nucleon (NN) interactions, the nuclear equations of state (EOSs) for neutron matter are calculated with the unitary correlation operator and high-momentum pair methods. Neutron matter is described using a finite particle number approach with magic number under a periodic boundary condition. The central short-range correlation originating from the short-range repulsion in the interaction is treated by the unitary correlation operator method (UCOM), and the tensor correlation and spin-orbit effects are described by the two-particle two-hole (2p2h) excitations of nucleon pairs, where the two nucleons with a large relative momentum are regarded as a high-momentum (HM) pair. With increasing 2p2h configurations, the total energy per particle of the neutron matter is well-converged under this UCOM+HM framework. Comparing the results calculated with AV4', AV6', and AV8' interactions, we demonstrate the effects of the short-range correlation, tensor correlation, and spin-orbit coupling on the density dependence of the total energy per particle of neutron matter. Moreover, the contribution of each Hamiltonian component to the total energy per particle is discussed. The EOSs of neutron matter calculated within the present UCOM+HM framework agree with the calculations of six microscopic many-body theories, especially the auxiliary field-diffusion Monte Carlo calculations.

Measurements of {Xi }{^-} and overline{Xi }{^+} production in proton\u2013proton interactions at sqrt{s_{NN}} = 17.3\xa0hbox {Ge}hbox {V} in the NA61/SHINE\xa0experiment

The production of Xi (1321)^{-} and overline{Xi }(1321)^{+} hyperons in inelastic p+p interactions is studied in a fixed target experiment at a beam momentum of 158 hbox {Ge}hbox {V}!/!c. Double differential distributions in rapidity {y} and transverse momentum p_{T} are obtained from a sample of 33M inelastic events. They allow to extrapolate the spectra to full phase space and to determine the mean multiplicity of both {Xi }{^-} and overline{Xi }{^+} . The rapidity and transverse momentum spectra are compared to transport model predictions. The {Xi }{^-} mean multiplicity in inelastic p+p interactions at 158 hbox {Ge}hbox {V}!/!c is used to quantify the strangeness enhancement in A+A collisions at the same centre-of-mass energy per nucleon pair.

J/\u03c8 production as a function of charged-particle multiplicity in p-Pb collisions at sqrt{s_{mathrm{NN}}} = 8.16 TeV

Inclusive J/ψ yields and average transverse momenta in p-Pb collisions at a center-of-mass energy per nucleon pair sqrt{s_{mathrm{NN}}} = 8.16 TeV are measured as a function of the charged-particle pseudorapidity density with ALICE. The J/ψ mesons are reconstructed at forward (2.03 < ycms< 3.53) and backward (−4.46 < ycms< −2.96) center-of-mass rapidity in their dimuon decay channel while the charged-particle pseudorapidity density is measured around midrapidity. The J/ψ yields at forward and backward rapidity normalized to their respective average values increase with the normalized charged-particle pseudorapidity density, the former showing a weaker increase than the latter. The normalized average transverse momenta at forward and backward rapidity manifest a steady increase from low to high charged-particle pseudorapidity density with a saturation beyond the average value.

Variational approach for pair optimization in the nucleon pair approximation

We propose a pair-condensate variational approach (PCV) to determine a set of the most important collective pairs in the description of low-lying states in atomic nuclei. Having available the precise details on these key collective pairs -- their spin, parity, and structure -- can be particularly useful in calculations based on the nucleon-pair approximation (NPA), helping to reduce their uncertainties. In trial calculations for the transitional Ba isotopes, our variational approach describes the evolution of quadrupole-deformation properties similar to Hartree-Fock treatments, while at the same time highlighting the $\gamma$ softness of $^{132}$Ba. Our approach can conclusively determine which collective pairs are critical for obtaining the lowest possible yrast, quasi-beta, quasi-gamma bands, producing both the level structure of these bands and related B(E2) values in reasonable consistency with experiment. These trial calculations suggest that with our PCV approach the NPA can be meaningfully applied to transitional nuclei with a wide spectrum of shapes. We also show that while neutron negative-parity pairs could in principle have an important impact on backbending in $^{132}$Ba, they are not favored for this nucleus.

Nucleon pair shell model in M scheme

The nucleon pair shell model (NPSM) is casted into the so-called M-scheme for the cases with isospin symmetry and without isospin symmetry. The odd system and even system are treated on the same foot. The uncoupled commutators for nucleon-pairs, which are suitable for M-scheme, are given. Explicit formula of matrix elements in M-scheme for overlap, one-body operators, two-body operators are obtained. It is found that the $cpu$ time used in calculating the matrix elements in M-scheme is much shorter than that in the J-scheme of NPSM.

Nuclear shape phase transition in even-even 158−168Hf isotopes

The interacting sdf-boson-approximation model is adopted to describe the low-lying positive and negative parity states in even-even 158−168Hf isotopes. The negative parity states are described using the sdf-IBM model by adding the L = 3 f-bosons nucleon pairs to the standard sd-boson model space. To determine the deformation of the nuclear structure of these isotopes the potential energy surfaces are calculated as functions of the deformation parameters. The reduced transition probabilities B(E2) in N = 94 are compared to the critical point symmetry X(5) predictions. In this chain, the sdf-boson interacting parameters are investigated and plotted against a number of neutrons. The shape phase transition from spherical 158Hf to well-deformed 168Hf nuclei is observed.

Global fluid fits to identified particle transverse momentum spectra from heavy-ion collisions at the Large Hadron Collider

Transverse momentum spectra of identified particles produced in heavy-ion collisions at the Large Hadron Collider are described with relativistic fluid dynamics. We perform a systematic comparison of experimental data for pions, kaons and protons up to a transverse momentum of 3 GeV/c with calculations using the FluiduM code package to solve the evolution equations of fluid dynamics, the TrENTo model to describe the initial state and the FastReso code to take resonance decays into account. Using data in five centrality classes at the center-of-mass collision energy per nucleon pair sqrt{s_{mathrm{NN}}} = 2.76 TeV, we determine systematically the most likely parameters of our theoretical model including the shear and bulk viscosity to entropy ratios, the initialization time, initial density and freeze-out temperature through a global search and quantify their posterior probability. This is facilitated by the very efficient numerical implementation of FluiduM and FastReso. Based on the most likely model parameters we present predictions for the transverse momentum spectra of multi-strange hadrons as well as identified particle spectra from Pb-Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV.

Quasielastic lepton scattering and back-to-back nucleons in the short-time approximation

Understanding quasielastic electron- and neutrino-scattering from nuclei has taken on new urgency with current and planned neutrino oscillation experiments, and with electron scattering experiments measuring specific final states, such as those involving nucleon pairs in ``back-to-back'' configurations. Accurate many-body methods are available for calculating the response of light ($A \leq 12$) nuclei to electromagnetic and weak probes, but they are computationally intensive and only applicable to the inclusive response. In the present work we introduce a novel approach, based on realistic models of nuclear interactions and currents, to evaluate the short-time (high-energy) inclusive and exclusive response of nuclei. The approach accounts reliably for crucial two-nucleon dynamics, including correlations and currents, and provides information on back-to-back nucleons observed in electron and neutrino scattering experiments. We demonstrate that in the quasielastic regime and at moderate momentum transfers both initial- and final-state correlations, and two-nucleon currents are important for a quantitatively successful description of the inclusive response and final state nucleons. Finally, the approach can be extended to include relativistic---kinematical and dynamical---effects, at least approximately in the two-nucleon sector, and to describe the response in the resonance-excitation region.

Diffractive dissociation of alpha particles as a test of isophobic short-range correlations inside nuclei

The CLAS collaboration at Jefferson Laboratory has compared nuclear parton distributions for a range of nuclear targets and found that the EMC effect measured in deep inelastic lepton-nucleus scattering has a strongly “isophobic” nature. This surprising observation suggests short-range correlations between neighboring n and p nucleons in nuclear wavefunctions that are much stronger compared to p−p or n−n correlations. In this paper we propose a definitive experimental test of the nucleon-nucleon explanation of the isophobic nature of the EMC effect: the diffractive dissociation on a nuclear target A of high energy He4 nuclei to pairs of nucleons n and p with high relative transverse momentum, α+A→n+p+A′+X. The comparison of n−p events with p−p and n−n events directly tests the postulated breaking of isospin symmetry. The experiment also tests alternative QCD-level explanations for the isophobic EMC effect. In particular it will test a proposal for hidden-color degrees of freedom in nuclear wavefunctions based on isospin-zero [ud] diquarks.

Short-Range NN Correlations in the Reaction 12C + p → 10A + pp + N

The exclusive reaction 12C(p,pNN)10A of the quasi-elastic knockout of a nucleon from short-range correlated nucleon pair $$\langle NN\rangle $$ in the 12С nucleus by a proton with an energy of several gigaelectronvolts is considered in the plane-wave approximation. The translational invariant shell model with intermediate coupling is used to calculate two-nucleon spectroscopic factors for the $$\langle NN\rangle $$ pairs. Relativistic effects in the p + $$\langle NN\rangle $$ → p + N + N process are considered within light front dynamics.

Exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits

The exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits, which is an extension of the widely used standard (two-body) pairing model, is derived based on the Bethe–Richardson–Gaudin approach. The Bethe–Richardson–Gaudin equations in determining eigenstates and the corresponding eigen-energies of the model are provided and exemplified with up to three-pair interactions. With a suitable parameterization of the overall multi-pair interaction strengths, the model with one adjustable parameter and valence nucleons confined in the $$1d_{5/2}$$ and $$0g_{7/2}$$ orbits is applied to fit binding energies of $$^{102{\text {--}}112}$$Sn. It is shown that the ground-state occupation probabilities of nucleon pairs calculated from this model and those from the standard pairing model are almost the same with perfect ground-state overlap of the two models. A noticeable feature of the multi-pair interactions is that the even–odd staggering of pairing interaction strength appearing in the standard pairing model due to the Pauli-blocking is suppressed. As the result, the pairing interaction strength of the model only depends on the number of valence nucleon pairs in the system.

Kinetic freeze-out in central heavy-ion collisions between 7.7 and 2760 GeV per nucleon pair

We fit the single-particle pt spectra of identified pions, kaons, and (anti)protons from central collisions of gold or lead nuclei at energies between 7.7 and 2760 GeV per nucleon pair. The blast wave model with included resonance production and with an assumption of partial chemical equilibrium is used and the fits are performed with the help of a Gaussian emulator process. A kinetic freeze-out temperature is found about 100 MeV for the lowest collision energies and 80 MeV at the LHC. The average transverse expansion velocity grows with increasing from 0.45 to 0.65. Due to partial chemical equilibrium, the influence of resonance decays on the shape of the pt spectra for above 27 GeV is small.

Probing the core of the strong nuclear interaction.

The strong nuclear interaction between nucleons (protons and neutrons) is the effective force that holds the atomic nucleus together. This force stems from fundamental interactions between quarks and gluons (the constituents of nucleons) that are described by the equations of quantum chromodynamics. However, as these equations cannot be solved directly, nuclear interactions are described using simplified models, which are well constrained at typical inter-nucleon distances1-5 but not at shorter distances. This limits our ability to describe high-density nuclear matter such as that in the cores of neutron stars6. Here we use high-energy electron scattering measurements that isolate nucleon pairs in short-distance, high-momentum configurations7-9, accessing a kinematical regime that has not been previously explored by experiments, corresponding to relative momenta between the pair above 400 megaelectronvolts per c (c, speed of light in vacuum). As the relative momentum between two nucleons increases and their separation thereby decreases, we observe a transition from a spin-dependent tensor force to a predominantly spin-independent scalar force. These results demonstrate the usefulness of using such measurements to study the nuclear interaction at short distances and also support the use of point-like nucleon models with two- and three-body effective interactions to describe nuclear systems up to densities several times higher than the central density of the nucleus.

Studies of J/\u03c8 production at forward rapidity in Pb\u2013Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV

The inclusive J/ψ production in Pb–Pb collisions at the center-of-mass energy per nucleon pair sqrt{s_{mathrm{NN}}} = 5.02 TeV, measured with the ALICE detector at the CERN LHC, is reported. The J/ψ meson is reconstructed via the dimuon decay channel at forward rapidity (2.5 < y < 4) down to zero transverse momentum. The suppression of the J/ψ yield in Pb–Pb collisions with respect to binary-scaled pp collisions is quantified by the nuclear modification factor (RAA). The RAA at sqrt{s_{mathrm{NN}}} = 5.02 TeV is presented and compared with previous measurements at sqrt{s_{mathrm{NN}}} = 2.76 TeV as a function of the centrality of the collision, and of the J/ψ transverse momentum and rapidity. The inclusive J/ψ RAA shows a suppression increasing toward higher transverse momentum, with a steeper dependence for central collisions. The modification of the J/ψ average transverse momentum and average squared transverse momentum is also studied. Comparisons with the results of models based on a transport equation and on statistical hadronization are carried out.